Distance and displacement

• The distance covered by a moving object is the actual length of the path followed by the object, irrespective of the direction in which the body travels.
• So, Distance is a scalar quantity. SI unit of distance is meter.
• Displacement is the shortest distance covered by a moving object from the point of reference (initial position of the body), in a specific direction. i.e., it is a straight line between the initial position and the final position of the body, along with the direction.
• SI unit of displacement is metre.
• Displacement is a vector, i.e., the displacement is given by a number with proper units and direction.

Examples:

1. A ball is thrown vertically upwards to a vertical height ‘h’ and caught back by the thrower. Then distance = h + h = 2 h. But displacement = h – h = 0.

2. Suppose a ball is thrown vertically upward from the top of a tower of height h. Let the stone reach the bottom of the tower. Then distance travelled = H + H + h = 2H + h. But the displacement of the stone = –h.

3. When a particle completes one rotation in a circular path of radius r, the distance traveled = 2πr. But the displacement = 0, because the initial and final positions are the same. Suppose the particle traveled only from A to B. Then distance = πr, but displacement = 2r.

4. A particle moves from A to C through B. The distance travelled is 4 m + 3 m = 7 m. But displacement

Distances add algebraically. But displacements add geometrically

Comparison between distance and displacement:

• Distance is a scalar quantity and displacement is a vector quantity.
• Distance is always positive. Displacement can be +ve, zero or –ve.
• The actual distance covered by a particle can be equal to or greater than the magnitude of the displacement.
• The displacement of a particle between two points is a unique path, which can take a particle from its initial position to the final position.
• The displacement of a particle does not tell us anything about the nature of motion of the particle.
• The magnitude of displacement is equal to minimum possible distance between two positions.
• Distance ≥|Displacement|.
• For a moving particle distance can never be negative or zero while displacement can be zero. Zero displacement means that body after motion has come back to initial position).
• Distance > 0 but Displacement > = or < 0
• There are infinite possibilities of traversing or moving from one given point to another. But displacement is single valued while distance depends on actual path and so can have many values.
• For a moving particle distance can never decrease with time while displacement can. Decrease in displacement with time means body is moving towards the initial position.
• Magnitude of displacement can be equal to distance only if motion is along a straight line without change in direction.